∫ (4 - 9x^2)^- 1/2 dx =?

Question

∫ (4 - 9x^2)^- 1/2 dx =?

homework solutions (I got e for an answer)....

a. (1/3)Sin-1 (3x/2) + C

b. (1/2)Sin-1 (2x/3) + C

c. (1/3)Sin-1 (3x/4) + C

d. (1/4)Sin-1 (2x) + C

e. (1/4)Sin-1 (4x/3) + C

f. (1/2)Sin-1 (x/2) + C

g. none of these

Answer 1

∫ (4 - 9x^2)^- 1/2 dx
= ∫ 2^-1[1 - (3/2 x)^2]^- 1/2 dx
= ∫ 2^-1(2/3)[1 - (3/2 x)^2]^- 1/2 d3x/2
= (1/3)Sin-1 (3x/2) + C

Answer 2

FWIW, I got the same answer as Shasjing. I think it's answer a.


Doug

Answer 3

i got E too...